The Erdős Problems Site Stopped Saying Which Ones Are Solved

In 1931, at eighteen, Paul Erdős asked a question about whole numbers whose sums never repeat. He later called it “perhaps my first serious problem”. On erdosproblems.com, the website that collects his problems, it is number 1, with a $500 prize attached. In September its page carried a word in capitals above the statement: DISPROVED. Today the word is gone, and so is every other label on the site. Since 6 October none of its 1,221 problems says whether it is open or solved.

The question is simple to state. Pick n different whole numbers so that no two different groups of them add up to the same total; the powers of two, 1, 2, 4, 8 and so on, are the obvious example. How small can the largest number be? Erdős suspected that you could never do much better than the powers of two: the largest number would always be at least some fixed fraction of 2 to the power n. A pre-release OpenAI model, GPT-6 Astra, showed otherwise. However small the fraction you choose, there are ever larger sets that beat it. The proof was checked in Lean, a language in which a computer verifies every step.

The disproof came out of a test. On 6 September Epoch AI, a group that measures what AI systems can do, posted FrontierMath Erdős: 68 problems still open in August, taken from the 652 open ones on the site, which a model has to settle in Lean on its own. The co-author who chose the 68 is Thomas Bloom, the University of Manchester mathematician who created erdosproblems.com in 2023 and still runs it. Under the benchmark’s rules, with $300 per problem, GPT-6 Astra scored 3% and four other models scored zero. In larger attempts outside those rules it also disproved problem 1. The five problems it resolved took more than $220,000 of compute across all attempts, the paper says.

The site recorded the result in stages, as the Internet Archive shows. On 3 September the page for problem 1 read “DISPROVED (FORMALIZED)”, with the note “No explanation available”. By 18 September it read “DISPROVED (LEAN)”: solved in the negative, proof verified by computer. Below the statement sits an exposition written by Bloom himself, last edited on 3 September, to help mathematicians “quickly understand the main ideas”. Working through it, he writes, he found links to a 1929 result of Carl Ludwig Siegel’s that were “obscured in the original GPT proof”.

On 6 October Bloom explained the change. When he added comments in August 2025, a community formed around the problems; the site now typically gets between 10,000 and 25,000 unique visitors a day. But the main public use of it, he writes, has become advertising AI-generated proofs, “often without any attempt to explain them”, to stake “a (increasingly meaningless) priority claim”. So he has frozen new comments and proof claims on problems, removed the statuses and the count of solved problems, and dropped the language of credit. Places that store AI proofs should exist, he says, but apart from a site meant to keep the questions alive: “Just as one does not open a restaurant in an abattoir…” Removing “solved” is meant to discourage people “copying problems into their AI to get an OPEN->SOLVED dopamine hit”. It is also, in his view, “against the spirit of Erdős to regard any problem as ‘closed’”.

This note checked the site on 7 October. The page for problem 1 has no label, and the “Random Solved” and “Random Open” buttons it had in September have become a single “Random”. Even the old addresses that filtered problems by status now return the same thing: the sixteen problems tied to a single entry in Erdős’s bibliography appear identically under /solved, /open and /all. The homepage gives one number: 1,221 problems in the database. The prose stays. Problem 1 still says it “was disproved by GPT-6 Astra”, because the new rule covers future results: where he once would have written “Bloom proved that x > y”, Bloom says he will write “It is known that x > y”, with a link to whoever explained the proof.

Not checked: the correctness of the proof, which this note did not examine; what the page showed between 18 September and 6 October; whether the homepage used to display a solved count, since the Internet Archive was unreachable during this check (Bloom’s post says the count and percentage will no longer be shown). The same day as his post, OpenAI published a batch of new mathematical results from an internal model on GitHub. A month after helping build a test that measures AI on these problems, the person who runs the site has stopped showing that measurement on its pages. All 1,221 problems are still there, in the same neutral colour.